Equilibrium dividend strategies in the dual model with a random time horizon  

作　　者：ZHAO Yong-xia YE Chuan-xiu CHENG Gong-pin 

机构地区：[1]School of Statistics and Data Science,Qufu Normal University,Qufu 273165,China [2]School of Mathematical Sciences,Qufu Normal University,Qufu 273165,China [3]School of Economics,Nanjing University of Finance and Economics,Nanjing 210046,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2023年第4期510-522,共13页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the Shandong Provincial Natural Science Foundation of China(ZR2020MA035 and ZR2023MA093)。

摘　　要：This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.

关 键 词：equilibrium dividend strategies non-exponential discounting time inconsistence dual model equilibrium HJB-equation 

分 类 号：F830.91[经济管理—金融学] O213[理学—概率论与数理统计]